17372 ÷ 5 = 3474 R2
Alright, let's work through the division of 17372 by 5 step by step.

Step 1:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 5

Step 2:
5 goes into 17 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 15 from 17 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 5

Step 3:
5 goes into 23 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 34
Subtract 20 from 23 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 5

Step 4:
5 goes into 37 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 347
Subtract 35 from 37 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 5

Step 5:
5 goes into 22 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 3474
Subtract 20 from 22 to get 2.

The final result is 3474 with a remainder of 2.